Find the volume of the irregular
figure.
1 cm
4 cm
3 cm 1 cm
9 cm
?] cm
5 cm

As a result, the slope is 1/5 and the y-intercept is 2, and the equation is written in slope-intercept form as y = (1/5)x + 2.

On a two-dimensional coordinate plane, the equation of a line is shown using the slope-intercept form. Y = mx + b, where m is the line's slope and b is the y-intercept, is how the equation is expressed. The pace at which the line is rising or dropping is indicated by the slope (m). It is the ratio of any two places on the line's vertical change (rise) to horizontal change (run). In other words, it informs you of the line's steepness. The line is rising from left to right if the slope is positive, and descending from left to right if the slope is negative.

given

We must find y in order to convert the equation 2x - 10y = -20 into slope-intercept form, which is represented by the formula y = mx + b, where m is the slope and b is the y-intercept.

2x - 10y = -20

Initially, we must separate the y term from the other terms by deducting 2x from both sides:

-10y = -2x - 20

The next step is to separate y by multiplying both sides by -10:

y = (2/10)x + 2

When we simplify the fraction, we obtain:

y = (1/5)x + 2

As a result, the slope is 1/5 and the y-intercept is 2, and the equation is written in slope-intercept form as y = (1/5)x + 2.

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Hi!

The ratio in the picture is 3:12. There are 3 tbsp of vinegar for every 12 tbsp of water.

[tex]\frac{3}{12}[/tex] can be simplified to [tex]\frac{1}{4}[/tex] by dividing the numerator and denominator by 3.

1 cup of vinegar to 4 cups of water is also [tex]\frac{1}{4}[/tex].

Therefore, they are equal and the ratio is maintained.

(NOTE: the unit of measurement DOES not matter - they're still equivalent)

For another problem:

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Answer:

5 yards

Step-by-step explanation:

15/3=5

Answer:

1. x = 56

2. y = 2

3. x = 6

4. y = 3

5. k = 10.2

6. w = 21

7. x = 72

Step-by-step explanation:

1. x + 4 = 60

x = 56

2. 3y - 2 = 4

3y = 6

y = 2

3. 3x - 7 = 11

3x = 18

x = 6

4. 5y + 3 = 18

5y = 15

y = 3

5. 3 + 6k = 64

6k = 61

k = 10.2

6. w ÷ 3 - 5 = 2

w ÷ 3 = 7

w = 21

7. x ÷ 8 + 3 = 12

x ÷ 8 = 9

x = 72

[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]

[tex]\bold{\red{ x + 4 = 60 }}[/tex]

[tex]\sf{ x = 60 - 4 }[/tex]

[tex]\bold{ x = 56 }[/tex]

Hence , The value of x is 56 .

[tex]\bold{\red{ 3y - 2 = 4 }}[/tex]

[tex]\sf{ 3y = 4 + 2 }[/tex]

[tex]\sf{ 3y = 6}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{6}{3}}}[/tex]

[tex]\bold{ y = 2 }[/tex]

Hence , The value of y is 2 .

[tex]\bold{\red{ 3x - 7 = 11 }}[/tex]

[tex]\sf{ 3x = 11 + 7 }[/tex]

[tex]\sf{ 3x = 18}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{18}{3}}}[/tex]

[tex]\bold{ x = 6 }[/tex]

Hence , The value of x is 6 .

[tex]\bold{\red{ 5y + 3 = 18 }}[/tex]

[tex]\sf{ 5y = 18 - 3 }[/tex]

[tex]\sf{ 5y = 15}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{15}{5}}}[/tex]

[tex]\bold{ y = 3 }[/tex]

Hence , The value of y is 3 .

[tex]\bold{\red{ 3 + 6k = 64 }}[/tex]

[tex]\sf{ 6k = 64 - 3 }[/tex]

[tex]\sf{ 6k = 61}[/tex]

[tex]\bold{ k = }{\sf{\dfrac{61}{6}}}[/tex]

Hence , The value of k is 61/6 .

[tex]\bold{\red{\dfrac{W}{3}}}{\bold{\red{ - 5 = 2 }}}[/tex]

[tex]\sf{\dfrac{W - 15}{3}}{\sf{ = 2 }}[/tex]

[tex]\sf{ W - 15 = 2}{\sf{\times{ 3 }}}[/tex]

[tex]\sf{ W - 15 = 6 }[/tex]

[tex]\sf{ W = 6 + 15 }[/tex]

[tex]\bold{ W = 21}[/tex]

Hence , The value of W is 21 .

[tex]\bold{\red{\dfrac{x}{8}}}{\red{\bold{ + 3 = 12 }}}[/tex]

[tex]\sf{\dfrac{x + 24 }{8 }}{\sf{ = 12 }}[/tex]

[tex]\sf{ x + 24 = 12}{\sf{\times{ 8 }}}[/tex]

[tex]\sf{ x + 24 = 96 }[/tex]

[tex]\sf{ x = 96 - 24 }[/tex]

[tex]\bold{ x = 72 }[/tex]

Hence, The value of x is 72 .

Answer:

x=2

Step-by-step explanation:

18−7x=2x

Step 1: Simplif

18−7x=2x

18+−7x=2x

−7x+18=2x

Step 2: Subtract 2x from both sides.

−7x+18−2x=2x−2x

−9x+18=0

Step 3: Subtract 18 from both sides.

−9x+18−18=0−18

−9x=−18

Step 4: Divide both sides by -9.

Answer:

2

Step-by-step explanation:

hope it helps.........

Answer:

total bill amount + tip = $77.21

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Let's say the amount of bushes sold (yield) is b, and the price per bushel is p.

When calculating total revenue, we want to multiply price by quantity. Quantity here is b, and price is p. Therefore, p*q = revenue = return.

Let's say that the amount of weeks is w.

Price after w weeks = 24 - 1.50 for each week = 24 - 1.50w

Yield after w weeks = 4 + 0.5 for each week = 4 + 0.5w

Revenue after w weeks = p * b = (24-1.50w) * (4+0.5w) = 96 - 6w + 12w - 0.75w² = -0.75w²+6w + 96.

We want to maximize revenue. First, we can find when the derivative of the function is 0.

d/dw(-0.75w²+6w + 96) = -1.5w + 6 = 0

subtract 6 from both sides

-1.5w = -6

divide both sides by -1.5 to isolate w

w = 4

plug that into our equation

-0.75(4)²+6(4) + 96 = -12 + 24 + 96 = 108

Because this function has a negative coefficient for the w², we can say that it is a parabola opening up downward, so when the derivative = 0, we have found the maximum of the function. Therefore, 4 is our answer

Answer:

i) see attached diagram

ii) 400 N

Step-by-step explanation:

Since we don’t know the mass of the seesaw, take moments about M (so we don’t have to consider R or mg).

Moment = Force x Perpendicular Distance to the Pivot

As the system is in equilibrium, total anti-clockwise moment = total clockwise moment:

⇒ 300 × 0.8 = b × 0.6

⇒         0.6 b = 240

⇒               b = 400 N

Answer:

Step-by-step explanation:

1 yard = 3 feet    

1/3          3/3    

1/3 yard = 1 feet

3ft * 5 yards = 15ft

1/3yard * 2 = 2/3yard        1ft * 2/3 = 2ft

15ft+2ft=17ft

Answer:

y = 28°

Step-by-step explanation:

The triangle is a right triangle which has 90 degrees.

The 3x falls under 90 degrees.

So:

→ 2y + 90° + 34° = 180°

→ 2y = 180° - 124°

→ 2y = 56°

→ y = 28°

Triangle

XYZ = right triangle

3x = 90°

X + Y + Z = 180°

34° + 3x + 2y = 180°

34° + 90° + 2y = 180°

2y = 180° - (34° + 90°)

2y = 56°

y = 28°

Answer:

105 minutes

Step-by-step explanation:

The pond is a prism. Its volume is the area of the trapezoidal base (the front and back faces) multiplied by the height (the 1 m edge).

Area of base of pond (front face) = (1/2)(B + b)h

Base = (1/2)(1.5 m + 0.6 m)(2 m)    [Here, height is the height oif the trapezoid, so it is 2 m]

Base = 2.1 m²

Volume = Base × Height

Volume = 2.1 m² × 1 m    [Here, height is the height of the prism, so it is 1 m]

Volume = 2.1 m³

The volume of the upper 30 cm (= 0.3 m) of the pond is:

V = LWH

V = 2 m × 1 m × 0.3 m

V = 0.6 m³

The volume of water decreased 0.6 m³ in 30 minutes.

In 60 minutes, it would decrease by 1.2 m³.

60 minutes = 1 hour

The flow rate is 1.2 m³ / hour.

The total volume of the pond is 2.1 m³.

Emptying out the pond completely means removing 2.1 m³ of water at the flow rate of 1.2 m³/hour.

flow rate = volume/time

time × flow rate = volume

time = volume / flow rate

time = 2.1 m³ / 1.2 m³/hour = 1.75 hour

time = 1.75 hour × 60 minutes/hour = 105 minutes

Answer: 105 minutes

Answer : When input is n, ouput is n+2.

Answer:

x must be 4

Step-by-step explanation:

Write and solve an equation of ratios.  Start with the ratio of the hypotenuses:  

 x + 2         x

----------- = --------

 x + 5        x + 2

Cross multiplying results in (x + 2)^2 = x^2 + 5x

performing the indicated squaring, (x + 2)^2 = x^2 + 4x + 4.  And therefore:

x^2 + 4x + 4 = x^2 + 5x

Simplifying, we get 4x + 4 = 5x, so x must be 4

hypotenuse (h)=?

perpendicular (p)=3

base(b)=2

using pythagoras theorem

h²=p²+b²

h²=3²+2²

h²=9+4

h²=13

h=√13

using pythagoras theorem

b²=h²-p²

b²=12²-10²

b²=144-100

b=√44

b=2√11

Answer:

Hope this helps.

Answer:

VVV

Step-by-step explanation:

A number that is increased by 50% and then decreased by 50% is called sequential percentage calculation or successive percentage calculation.

50 percent minus 50 percent is 0 percent, but you cannot simply take 0 percent of a number to get the correct answer when you want to increase a number by 50 percent and then decrease the result by 50 percent.

Answer:

  5/6

Step-by-step explanation:

Assuming everyone identifies as female or male, the fraction is ...

  female / (female + male)

  5/(5 +1) = 5/6

5/6 of the students are female in the math course.

That all added is 9/4 so now just turn that into pounds. goodluck :)

Answer:

2 1/4

Step-by-step explanation:

You can add together all of the numerators to get 9/4 which simplifies to be 2 1/4.

Answer:

option C gives, x = 8

Step-by-step explanation:

A.

[tex]\frac{5}{2}x+\frac{7}{2}=\frac{3}{4}x+14[/tex]

[tex]\frac{5}{2} x-\frac{3}{4} x = 14-3.5[/tex]

[tex]\frac{10}{4} x-\frac{3}{4} x = 10.5[/tex]

[tex]\frac{7}{4} x = 10.5[/tex]

[tex]x=\frac{10.5*4}{7}[/tex]

[tex]x = 6[/tex]

B.

[tex]\frac{5}{4}x-9=\frac{3}{2}x-12[/tex]

[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex]

[tex]\frac{5-6}{4} x = -3[/tex]

[tex]-x = 4(-3)[/tex]

[tex]x =12[/tex]

C.

[tex]\frac{5}{4}x-2=\frac{3}{2}x-4[/tex]

[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex]

[tex]\frac{5}{4}x-\frac{6}{4}x=-2[/tex]

[tex]-x = (-2)*4[/tex]

[tex]x=8[/tex]

D.

[tex]\frac{5}{2} x-7 = \frac{3}{4}x+14[/tex]

[tex]\frac{5}{2} x-\frac{3}{4}x = +14+7[/tex]

[tex]\frac{10}{4} x-\frac{3}{4}x = +21[/tex]

[tex]\frac{7}{4} x=21[/tex]

[tex]x= \frac{21*4}{7}[/tex]

[tex]x = 12[/tex]

Answer:

x = 3

Step-by-step explanation:

Answer:

t4 + 42.5 = c

Step-by-step explanation:

Hi!

I can help you with joy!

Area of a Rectangle= Length times the Width

Multiply [tex]\displaystyle\frac{1}{2}[/tex] times [tex]\displaystyle\frac{2}{21}[/tex]

Guide to Multiplying Fractions

Recall that we multiply the numerator times the numerator.

After that, we multiply the denominator times the denominator.

[tex]\displaystyle\frac{1}{2} *\frac{2}{21}[/tex]

[tex]\displaystyle\frac{1*2}{2*21}[/tex]

[tex]\displaystyle\frac{2}{42}[/tex] = [tex]\displaystyle\frac{1}{21}[/tex] (Answer) I hope this helps!

[tex]\bf{ContentGirl[/tex]

[tex]\bf{ElatedTeen[/tex]

Ask me if you have any doubts or queries. :)

Answer:

Option B

Step-by-step explanation:

Given the following question:

9 is 10 times the value
29,461 ⇒ thousands place
[tex]100\times10=1000[/tex]

Your answer is option B or "53,982". Since the nine is in the hundred's place, and one-hundred times ten, is equal to a thousand.

[tex]900\times10=9000[/tex]

Hope this helps.

The value of the digit 9 in the number 29,461 that is 10 times the value of the digit 9 is; B: 53,982

We are given the number 29461.

In the given number;

1 is units

6 is tens

4 is hundred

9 is thousands

2 is ten thousands

This means any number that will has to be multiplied by 10 to give the 9000 above will have to be hundreds.

From the given options, only 53982 contains 9 in the hundreds position and so is correct.

Read more about Digits at; https://brainly.com/question/26856218

Answer:

your answer will be letter b

Step-by-step explanation:

Answer:

The answer is going to be 85.5 miles apart.

Step-by-step explanation:

if the first car is going 49 miles for every hour and the second at 68 we now have our two numbers. then we know its 4.5 hours so our equation goes like this.

(68*4.5)-(49*4.5)=y

We do our rules with pemdas and what not.

we get

306-220.5=y

We subtract and bam

y= 85.5 miles apart.

Hope this helps.

A brainliest is always appreciated

Answer:1,410,000

Step-by-step explanation: